Why is the government involved in marriage?

Seems this gay marriage debate would be over if the government would just stop recognizing marriage or officiating weddings. Any marriage that is on the books or made in the future could be recognized as a civil union. If two same people got married it would be a civil union. If a religious or secular institution wants to marry two people together that should be their business. The gov't will just take the civil union certificate as proof of union for tax and other law purposes. If conservatives are upset that two same people got married, they would only be able to redress their grievances with the institution that put them together. Any holes in that argument that you see?